Solving the ECG Forward Problem by Means of Standard h- and h-Hierarchical Adaptive Linear Boundary Element Method: Comparison With Two Refinement Schemes

The boundary element method (BEM) is a commonly used numerical approach to solve biomedical electromagnetic volume conductor models such as ECG and EEG problems, in which only the interfaces between various tissue regions need to be modeled. The quality of the boundary element discretization affects the accuracy of the numerical solution, and the construction of high-quality meshes is time-consuming and always problem-dependent. Adaptive BEM (aBEM) has been developed and validated as an effective method to tackle such problems in electromagnetic and mechanical fields, but has not been extensively investigated in the ECG problem. In this paper, the h aBEM, which produces refined meshes through adaptive adjustment of the elementspsila connection, is investigated for the ECG forward problem. Two different refinement schemes: adding one new node (SH1) and adding three new nodes (SH3), are applied for the h aBEM calculation. In order to save the computational time, the h-hierarchical aBEM is also used through the introduction of the h-hierarchical shape functions for SH3. The algorithms were evaluated with a single-layer homogeneous sphere model with assumed dipole sources and a geometrically realistic heart-torso model. The simulations showed that h aBEM can produce better mesh results and is more accurate and effective than the traditional BEM for the ECG problem. While with the same refinement scheme SH3, the h-hierarchical aBEM can save the computational costs about 9% compared to the implementation of standard h aBEM.